• International Journal of Concrete Structures and Materials
• /
• 제10권2호
• /
• pp.143-147
• /
• 2016

In recent years, some modifications were introduced in the stress-strain relationship of the steel in order to develop a more efficient shear model for reinforced concrete members. The last contribution in this sense corresponding to the Refined Compression Field Theory (RCFT, 2009); this theory proposed a steel constitutive model that has account the tension stiffening area prescribed by technical codes, what simplifies all the design process. However, under certain design conditions supported by such codes, the RCFT model does not provide a real (non-complex) solution for the steel yield strain when the prescribed tension stiffening area is considered; then the load-strain response cannot be computed. In this technical note, the tension stiffening area is fixed in order to guarantee the application of the embedded steel constitutive model for all the standard design range.

• Computers and Concrete
• /
• 제17권1호
• /
• pp.29-51
• /
• 2016

Tension-stiffening is the contribution of concrete between the cracks to carry tensile stresses after cracking in Reinforced Concrete (RC) members. In this paper, a tension-stiffening model has been proposed for computationally efficient nonlinear analysis of RC flexural members subjected to service load. The proposed model has been embedded in a typical cracked span length beam element. The element is visualized to consist of at the most five zones (cracked or uncracked). Closed form expressions for flexibility and stiffness coefficients and end displacements have been obtained for the cracked span length beam element. Further, for use in everyday design, a hybrid analytical-numerical procedure has been developed for nonlinear analysis of RC flexural members using the proposed tension-stiffening model. The procedure yields deflections as well as redistributed bending moments. The proposed model (and developed procedure) has been validated by the comparison with experimental results reported elsewhere and also by comparison with the Finite Element Method (FEM) results. The procedure would lead to drastic reduction in computational time in case of large RC structures.

• Structural Engineering and Mechanics
• /
• 제5권5호
• /
• pp.507-521
• /
• 1997

The ultimate behavior of a reinforced concrete hyperbolic paraboloid saddle shell under uniformly distributed vertical load is investigated using an inelastic, large displacement finite-element program originally developed at North Carolina State University. Unlike with the author's previous study which shows that the saddle shell possesses a tremendous capacity to redistribute the stresses, introducing tension stiffening in the model the cracks developed are no longer through cracks and formed as primarily bending cracks. Even though with small tension stiffening effect, the behavior of the shell is changed markedly from the one without tension stiffening effect. The load-deflection curves are straight and the slope of the curves is quite steep and remains unchanged with varying the tension stiffening parameters. The failure of the shell took place quite suddenly in a cantilever mode initiated by a formation of yield lines in a direction parallel to the support-to-support diagonal. The higher the tension stiffening parameters the higher is the ultimate load. The present study shows that the ultimate behavior of the shell primarily depends on the concrete tensile characteristics, such as tensile strength (before cracking) and the effective tension stiffening (after cracking). As the concrete characteristics would vary over the life of the shell, a degree of uncertainty is involved in deciding a specified ultimate strength of the saddle shell studied. By the present study, however, the overload factors based on ACI 318-95 are larger than unity for all the cases studied except that the tension stiffening parameter is weak by 3 with and without the large displacement effect, which shows that the Lin-Scordelis saddle shell studied here is at least safe.

• 한국콘크리트학회:학술대회논문집
• /
• 한국콘크리트학회 2000년도 가을 학술발표회 논문집(II)
• /
• pp.873-878
• /
• 2000

Tension stiffening effects of reinforced concrete member with large diameter bar, mainly used at reactor building of nuclear power plant, are studied by uniaxial structural tests. Bond length and stress of steel bar, size of steel bar, and compressive strength of concrete are evaluated to tension stiffening by uniaxial tests. Problems and solution during the uniaxial test are suggested. The prevent splitting cracks, concrete cover-to-bar diameter ratio $c/d_{b}$ is kept 2.6~2.8. Because the bond length is increased as the size of steel bar, the specimen length of the D35 steel bar is required at least 2.0 m. The specimen length must be decided with bond length as well as concrete cover-to-bar diameter ratio to prevent splitting crack.

• Computers and Concrete
• /
• 제1권4호
• /
• pp.417-432
• /
• 2004

An analytical model which can simulate the post-cracking nonlinear behavior of reinforced concrete (RC) members such as bars and panels subject to uniaxial and biaxial stresses is presented. The proposed model includes the description of biaxial failure criteria and the average stress-strain relation of reinforcing steel. Based on strain distribution functions of steel and concrete after cracking, a criterion to consider the tension-stiffening effect is proposed using the concept of average stresses and strains. The validity of the introduced model is established by comparing the analytical predictions for reinforced concrete uniaxial tension members with results from experimental studies. In advance, correlation studies between analytical results and experimental data are also extended to RC panels subject to biaxial tensile stresses to verify the efficiency of the proposed model and to identify the significance of various effects on the response of biaxially loaded reinforced concrete panels.

• 산업기술연구
• /
• 제18권
• /
• pp.87-95
• /
• 1998

Cracking is considered to be one of the important factors in determining the durability of reinforced concrete structures. When the bending stress exceeds the modulus of rupture of the concrete, cracking form along the length of members. The total load is transferred across these cracks by the reinforcement, but the concrete between cracks is still capable of carrying stresses due to the bond between steel and concrete. This phenomenon is called the tension stiffening effect. The tension stiffening effect is affected by many variables, such as the bond stress, strength of concrete, interrocking of aggregate, type of steel, and dowel action of steel. Also, this tension stiffening effect is usually quite significant in beams under service loading, and must be taken into account in the calculation of deflection and crack widths. In this study, the experiment was carried out on types of specimen, strength of concrete, and steel ratio and finite element analysis were compared in terms of load-deflection relationship, crack pattern.

• Computers and Concrete
• /
• 제18권1호
• /
• pp.139-154
• /
• 2016

Since the concrete strength around the reinforcement rebar affects the tension stiffening, the tension stiffening effect of ultra high performance concrete on the concrete members reinforced by steel rebar is examined by testing the specimens with circular cross section with the length 850 mm reinforced by a steel rebar at the center of a specimen's cross section in this research. Conducting a tensile test on the specimens, the cracking behavior is evaluated and a curve with an exponential descending branch is obtained to explain the post-cracking zone. In addition, this paper proposes an equation for this branch and parameters of equation is obtained based on the ratio of cover thickness to rebar diameter (c/d) and reinforcement percentage (${\rho}$).

• Structural Engineering and Mechanics
• /
• 제81권3호
• /
• pp.349-365
• /
• 2022

Steel fibre-reinforced concrete (SFRC) is an emerging class of composite for construction. However, a reliable method to assess the flexural behaviour of SFRC structural member is in lack. An analytical technique is proposed for determining the moment-curvature response of concrete beams reinforced with steel fibres and longitudinal bars (R/SFRC members). The behaviour of the tensile zone of such members is highly complex due to the interaction between the residual (tension softening) stresses of SFRC and the tension stiffening stresses. The current study suggests a transparent and mechanically sound method to combine these two stress concepts. Tension stiffening is modelled by the reinforcement-related approach assuming that the corresponding stresses act in the area of tensile reinforcement. The effect is quantified based on the analogy between the R/SFRC member and the equivalent RC member having identical geometry and materials except fibres. It is assumed that the resultant tension stiffening force for the R/SFRC member can be calculated as for the equivalent RC member providing that the reinforcement strain in the cracked section of these members is the same. The resultant tension stiffening force can be defined from the moment-curvature relation of the equivalent RC member using an inverse technique. The residual stress is calculated using an existing model that eliminates the need for dedicated mechanical testing. The proposed analytical technique was validated against test data of R/SFRC beams and slabs.

• 콘크리트학회논문집
• /
• 제23권6호
• /
• pp.791-797
• /
• 2011

이 논문은 인장증강효과에 대한 피복두께의 영향을 알아보기 위하여 실시한 12개의 축하중을 받는 직접인장 실험체의 실험 결과를 정리 분석한 것이다. 피복두께와 철근 직경의 비를 주 변수로 선정하여 6개의 서로 다른 피복 두께를 갖는 실험체를 제작하여 실험을 실시하였다. 실험 결과에 따르면 피복두께가 얇을수록 쪼갬균열의 영향이 크게 나타났으며, 인장증강효과와 균열간격이 감소하였다. 그리고 균열안정화 단계에서의 인장증강효과도 피복두께가 얇아질수록 감소하는 것을 확인하였다. 현행 설계기준의 인장증강효과 모델들은 피복두께의 변화에 따른 인장증강 거동의 차이를 반영할 수 없으며, 특히 피복두께가 얇을수록 인장증강효과가 감소하는 현상을 고려하지 못하고 있다. 따라서 이 연구에서 수행한 실험 및 분석 결과를 근거로 하여 인장증강효과에 피복두께의 영향을 반영할 수 있는 인장증강 계수 수정식을 제안하였다.

• Structural Engineering and Mechanics
• /
• 제54권3호
• /
• pp.501-520
• /
• 2015

Presence of torsional loadings can significantly affect the flow of internal forces and deformation capacity of reinforced concrete (RC) columns. It increases the possibility of brittle shear failure leading to catastrophic collapse of structural members. This necessitates accurate prediction of the torsional behaviour of RC members for their safe design. However, a review of previously published studies indicates that the torsional behaviour of RC members has not been studied in as much depth as the behaviour under flexure and shear in spite of its frequent occurrence in bridge columns. Very few analytical models are available to predict the response of RC members under torsional loads. Softened truss model (STM) developed in the University of Houston is one of them, which is widely used for this purpose. The present study shows that STM prediction is not sufficiently accurate particularly in the post cracking region when compared to test results. An improved analytical model for RC square columns subjected to torsion with and without axial compression is developed. Since concrete is weak in tension, its contribution to torsional capacity of RC members was neglected in the original STM. The present investigation revealed that, disregard to tensile strength of concrete is the main reason behind the discrepancies in the STM predictions. The existing STM is extended in this paper to include the effect of tension stiffening for better prediction of behaviour of square RC columns under torsion. Three different tension stiffening models comprising a linear, a quadratic and an exponential relationship have been considered in this study. The predictions of these models are validated through comparison with test data on local and global behaviour. It was observed that tension stiffening has significant influence on torsional behaviour of square RC members. The exponential and parabolic tension stiffening models were found to yield the most accurate predictions.